Joint work with Shira Yadai and Zhixing You.
Abstract. A -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be many full -trees such that the product of any countably many of them is an -Souslin tree.
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Submitted to Journal of the London Mathematical Society, July 2023.
Accepted, May 2024.